Part 19

My over-riding passion in writing all of these
articles, and frankly in ultimately allowing Stanford Wong to publish my book; is so that players can
finally bridge the gaping and disappointingly wide chasm between the edge that their
de-randomized throws produce...and the profits that their skills should be generating.

Making the connection between the edge that you currently shoot with and the
profit that those same skills should be earning you; is actually
easier than it appears, although admittedly, most players will continue to make it unnecessarily difficult on
themselves.

This entire series is all about how to
safely make more money from your current skills. In most cases, that means showing you what you
could accomplish if you simply wagered on your current advantage the way it should be
bet.

I like to make as much
money with as little risk from my D-I skills as possible. I do that
by focusing the bulk of the money that
I’ve allocated on a per-hand basis, to those validated positive-expectations wagers that I know I am most
likely to collect from during the point-cycle.

The following chart will help you determine
where your own opportunities are; and when you regress your wagers at the optimal regression point,
this chart also shows what your true edge over these multi-number global-bets really is.

Your true edge, when broken out on a
per-roll basis, is critical in helping you determine the proper size of your
pre-regression wagers in relation to the boundaries of your current total gaming
bankroll.

Player-Edge

using Optimized Regression

SSR-7

SSR-8

SSR-9

7’s per 36-rolls

5.14

4.5

4.0

7-Out Probability/Roll

14.29%

12.50%

11.11%

Average

Point-Cycle

Roll-Duration

7

8

9

Average Rolls/PL or 7-Out Decision

4.2

5.0

5.8

Inside

Inside-numbers to 7’s ratio

3.6:1

4.1:1

4.75:1

Inside-number

Probability/Roll

51.19%

52.08%

52.78%

Optimal Hits before Regressing

1

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

2.00%

6.23%

12.36%

Overall

Edge-per-Roll

0.48%

1.25%

2.13%

Across

Across-numbers to 7’s ratio

4.8:1

5.6:1

6.4:1

Across-number

Probability/Roll

68.58%

70.00%

71.11%

Optimal Hits before Regressing

2

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.78%

5.84%

11.97%

Overall

Edge-per-Roll

0.42%

1.17%

2.06%

Outside

Outside-numbers to 7’s ratio

2.8:1

3.3:1

3.7:1

Outside-number

Probability/Roll

40.00%

40.83%

41.47%

Optimal Hits before Regressing

1

2

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.40%

5.10%

10.70%

Overall

Edge-per-Roll

0.33%

1.02%

1.85%

Even

Even-numbers to 7’s ratio

3.20:1

3.73:1

4.27:1

Even-number

Probability/Roll

45.72%

46.67%

47.42%

Optimal Hits before Regressing

1

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.82%

5.86%

12.09%

Overall

Edge-per-Roll

0.43%

1.17%

2.08%

Iron Cross

IC-numbers to 7’s ratio

6:1

7:1

8:1

IC-number

Probability/Roll

85.72%

87.50%

88.89%

Optimal Hits before Regressing

2

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.68%

5.59%

11.64%

Overall

Edge-per-Roll

0.40%

1.12%

2.01%

6 and 8

6’s & 8’s to 7’s ratio

2:1

2.33:1

2.67:1

6 & 8

Probability/Roll

28.57%

29.16%

29.63%

Optimal Hits before Regressing

2

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

2.42%

7.42%

14.00%

Overall

Edge-per-Roll

0.58%

1.48%

2.55%

5 and 9

5’s & 9’s to 7’s ratio

1.6:1

1.87:1

2.14:1

5 & 9

Probability/Roll

22.86%

23.33%

23.71%

Optimal Hits before Regressing

1

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.70%

5.60%

11.70%

Overall

Edge-per-Roll

0.40%

1.12%

2.02%

4 and 10

4’s & 10’s to 7’s ratio

1.2:1

1.4:1

1.6:1

4 and 10

Probability/Roll

17.14%

17.5%

17.78%

Optimal Hits before Regressing

1

2

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.10%

4.60%

9.60%

Overall

Edge-per-Roll

0.26%

0.92%

1.67%

What It Means

7’s per 36-rolls
is simply the average number of 7’s that will show up in a range of 36-rolls.
For a random-roller it is six 7’s per 36-rolls,
but as your Sevens-to-Rolls Ratio (SRR) improves, this number drops to 5.14 for
SRR-7, 4.5 for SRR-8, and 4.0 for SRR-9.

7-Out Probability/Roll represents the likelihood of a 7
showing up on any given roll. Given your SRR-rate, this can be expressed as a
percentage. For a random-roller, the probability of a 7 showing up on any given
roll is 16.67%, for a SRR-7 shooter it is 14.29%; for a SRR-8 dice-influencer it
is 12.5% on any given roll, and for a SRR-9 precision-shooter, it is 11.11%.

Point-Cycle Roll-Duration
is just another way of expressing your SRR-rate, in that it represents how many
roll, on average, you will see between 7’s.

Average Rolls/PL or 7-Out
Decision tells us
how many rolls our SRR-driven skill will generate before either repeating our
PL-Point or 7’ing-Out. Where this figure can be quite helpful is in figuring
out how many PL-Points we are likely to repeat during an average hand. The
reason this number is lower than our point-cycle roll duration is due to those
hands where multiple PL-Point numbers are made within a string of point-cycle
rolls. A random-roller will experience about 3.4 rolls per Passline decision,
while an SRR-7 shooter will encounter an average of 4.2 rolls, an SRR-8
dice-influencer will throw an average of 5.0 rolls per Passline decision, and a
SRR-9 precision-shooter will experience about 5.8 rolls per PL decision.

(Global-bet) to 7’s ratiois the specific expected
hit-rate for each of these multi-number wagers (Inside, Outside, Even, etc.)
when compared to the frequency of 7’s for each SRR skill-level. For example,
we’d randomly expect to see 3.0 Inside-number hits for every one 7-Out,
and Inside-numbers have a random per-roll expectancy-rate of 50%; however a
SRR-7 player produces a slightly better Inside-Number expectancy of 51.19%
per-roll, and can expect 3.6 Inside-number hits for each 7-Out that he throws.
Likewise, random-rollers expect to see 4.0 Across-numbers for each 7-Out (where
the Across-wager accounts for 66.6% of all random outcomes); whereas in the
hands of an SRR-7 shooter, Across-numbers generally account for a slightly
higher 68.58% per-roll appearance-rate, but because of the lower frequency of
7’s, the SRR-7 shooter enjoys a much higher 4.8 Across-numbers-to-7’s ratio.

(Global-bet)
Probability-per-Roll
sets out, in general terms, what we can expect each of these bets to account for
as far as per-roll probability is concerned. For example, the Iron-Cross
(everything but the 7) accounts for 83.33% of all random outcomes (the 7
accounts for the other 16.67%). However, as your SRR-rate improves, so does the
per-roll probability of this wager. For example, an SRR-7 shooter can expect
his I-C anything-but-7 outcomes to account for
85.72% of his outcomes, while the SRR-8 shooter can expect it 87.50% of the
time; and for the SRR-9 shooter, the Iron Cross will account for 88.89% of his
point-cycle results.

Optimal Hits Before Regressingis the number of
winning hits this particular bet should remain at its initial large
pre-regression level before optimally reducing it to a lower bet-amount. For
example, a SRR-7 shooter would ideally leave his Inside-Number wager at its
large pre-regression starting value for one hit only; while the SRR-8 shooter
can afford to leave it at its initial starting value for three paying hits
before regressing to a lower amount of exposure.

Cumulative Pre-Regression Edge on
this Wager based on Bet-Survival Curve is the aggregate advantage the
player has over the house prior to regressing his chosen bet at the optimal
time. This figure gives you an idea of how powerful regression-betting can be
when properly combined with dice-influencing. By merging your skill-driven
expected-roll-duration with a betting-method that utilizes and exploits the
fattest, highest-survival portion of your point-cycle expectancy-curve; you
derive benefit from the most frequently occurring opportunities, while
concurrently reducing bankroll volatility and risk as your point-cycle
bet-survival rate diminishes.

Overall Edge-per-Roll
is the weighted advantage you have over the house during each toss in your
point-cycle roll when using regression-style wagering. To manage volatility and
err on the ultra-conservative side of money management; this figure is used to
indicate how much of your total gaming bankroll you can reasonably afford to
expose to these multi-number global-wagers when starting with a larger initial
bet and then reducing it at the optimal regression point.

For example, an SRR-7 shooter who
validates his edge over the Place-bet 6 & 8 and chooses to use a 5:1 steepness
ratio ($30 each on the 6 & 8 regressed down to $6 each after the first hit);
would divide his 0.58% regression-based true edge over this combined bet into
the total initial bet-value of $60 ($60 / 0.0058) to determine that his
totalI-will-give-up-craps-if-I-lose-this-amount-of-money gaming
bankroll should be around $10,344 for this skill-level and regressed steepness
ratio.

Likewise, an SRR-8 player making
the very same bet, but with a 1.48% edge-per-roll over the Place-bet 6 & 8
wager, would optimally have a total
I-will-give-up-craps-if-I-lose-this-amount-of-money gaming bankroll of $4054
for this wager ($60 / 0.0148). If let’s say, this same player decided to use a
more modest 3:1 steepness ratio ($18 each on the 6 & 8 regressed down to $6 each
after optimally enjoying three paying hits at the initial rate); then he’d take
the total initial wager of $36 ($18 on the Place-bet 6 + $18 on the Place-bet 8)
and divide that by the same 0.0148 (his true regression-based edge per-roll over
this wager) to determine that he’d ideally have a total gaming bankroll of $2432
to back up this lower starting-value bet.

Coming Up

In Part Twenty of this series, we are
going to dive into the whole
how-much-money-do-I-REALLY-need-to-properly-exploit-my-edge question in
extraordinary detail. We’ll explore the best ways to safely utilize your edge
without imperiling your bankroll, and we’ll run through each of these
global-bets over a broad range of steepness-ratios to look at how big your
overall bankroll really should be.